Answer:
x = 5
∠L = 114°
∠ LMK = 31°
Step-by-step explanation:
In parallelogram, opposite sides are parallel and equal.
3x = 15
Divide both sides by 3
3x/3 = 15/3
x = 5
In parallelogram, opposite angles are equal
∠L = ∠J
∠L = 114°
In ΔJKM,
∠J + ∠JKM + ∠JMK = 180 {Angle sum property of triangle}
114 + ∠JKM + 35 = 180
149 + ∠JKM =180
∠JKM = 180 - 149
∠JKM = 31°
JK & ML are parallel and KM is transversal
Therefore, ∠ LMK = ∠JKM { oppoiste interior angles are congruent}
∠ LMK = 31°
